I'm not a fan of Titles so open for individual interpretation that easily results in thread hijacking.
Title is:
Is it your responsibility to report a coworker's drug use on the job?
Title should be:
Is it your responsibility to report a coworker's dangerous or illegal drug use on the job?
Of course the OP's intent was not someone taking aspirin for a headache, or someone's prescription medicine, or for that matter the person filling their coffee mugs down in the break room with caffeinated coffee. The OP is expecting one will immediately think it is referring to some drug that may affect job performance, might affect safety of them and others, or could affect overall company efficiency, or is societally illegal.
Thus, some people for decades have been nailed by others for during breaks, sneaking in snorts from hard liquor bottles in their coats. But then what about the driver that with lunch drank a single 8 ounce light beer? But because the OP used the word "drugs" they probably were not thinking of reporting those many historically that quietly drink alcohol when they think they can do so secretly. So if not alcohol, this must be some types of illegal drugs? Like one truck driver reporting on another driver they see shooting up with smack at a truck stop.
What about someone with a long weekend that on Monday morning takes a Ritalin tablet to stay awake? Or likewise a semitruck driver that on an employment important delivery, possibly feeling sleepy for whatever reason, very occasionally takes a like lower potency amphetamine during situations they don't want to fall asleep while driving and after which more coffee won't help. Much like military forces of all nations sometimes give their soldiers amphetamines only during long combat situations?
Well we can certainly imagine some situations where use of numbers of depressant drugs would endanger the rest of us while say driving their company vehicles in public. Or the employee that ignoring policy, smokes nicotine cigarettes in a restaurant kitchen when they think they are alone, where it might affect the flavor or prepared foods. But then what about that temporary minimum wage person during a work break sharing some other workers joint while working for the county cleaning vehicles at a motor pool?
Yeah a lot of situations. Because life can be complicated.